"Realise" is often a good translation for skjønne. Another translation for skjønne is something little kids say: "I don't get it!"

Å skjønne is related to that which is apparent (based on perception). Å forstå is related to that which is factual (can be proven).
The difference can be illustrated in the reading of a document in unfamiliar parlance (e.g., a high school student reading a legal brief), "I realise what it says, but I don't understand what it means," (Jeg skjønner det som står der, men jeg forstår ikke hva det betyr.)

Most of the time they're interchangeable.

Yes. That's correct, too. You can also say, "... ikke det som jeg sier."